The generator matrix

 1  0  1  1  1  6  1 12  1 10  1  1  8  1  1  1  1 14  1  1  4  2  1  1  1  1  0  0  1  6  1  1  1  0 12  6  1  1  1  1  1  1  6  4 10  1  2  1  2
 0  1 11  6 13  1 12  1  3  1 10  5  1  7  8  1 14  1  2 15  1  1 13  0  9  3  1  1 14  1  4 15 12  1  1  1  2  5  3  5  8  0  1  4  1 11  4  9 12
 0  0 12  0  4  0  0  8  0  8  8  8 12  4  4  4 12  4 12  0  4  4 12  8  8  8  8 12 12  8  4  0 12  0 12  0  4  8  4  0  4  0  8 12  0 12  4 12  8
 0  0  0  8  0  0  8  0  0  8  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  8  8  8  0  8  8  0  8  8  0  0  8  0  8  0  8  8  8  8  8  8  8  0  8
 0  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  0  8  0  8  8  0  0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  0  8  0  8  8  8
 0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  8  0  0  0  8  0

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+379x^44+192x^45+926x^46+496x^47+1818x^48+672x^49+1728x^50+512x^51+982x^52+160x^53+216x^54+16x^55+64x^56+8x^58+15x^60+2x^62+5x^64

The gray image is a code over GF(2) with n=392, k=13 and d=176.
This code was found by Heurico 1.16 in 3.87 seconds.